On the elimination of short-period terms in second-order general planetary theory investigated by Hori's method

1973 ◽  
Vol 25 (2) ◽  
pp. 271-354 ◽  
Author(s):  
Jean Meffroy
Keyword(s):  
Second Order ◽  
Planetary Theory ◽  
Short Period ◽  
General Planetary Theory

scholarly journals First order normalization in the generalized photo gravitational non-planar restricted three body problems

2015 ◽  
Vol 3 (2) ◽  
pp. 46
Author(s):  
Nirbhay Kumar Sinha
Keyword(s):  
Oblate Spheroid ◽  
Second Order ◽  
Elliptic Motion ◽  
First Order ◽  
Short Period ◽  
Order Part ◽  
Three Body

<p>In this paper, we normalised the second-order part of the Hamiltonian of the problem. The problem is generalised in the sense that fewer massive primary is supposed to be an oblate spheroid. By photogravitational we mean that both primaries are radiating. With the help of Mathematica, H<sub>2</sub> is normalised to H<sub>2</sub> = a<sub>1</sub>b<sub>1</sub>w<sub>1</sub> + a<sub>2</sub>b<sub>2</sub>w<sub>2</sub>. The resulting motion is composed of elliptic motion with a short period (2p/w<sub>1</sub>), completed by an oscillation along the z-axis with a short period (2p/w<sub>2</sub>).</p>

scholarly journals An Iterative Method of General Planetary Theory

1974 ◽  
Vol 62 ◽  
pp. 139-155
Author(s):  
V. A. Brumberg
Keyword(s):  
Power Series ◽  
Equations Of Motion ◽  
Slight Modification ◽  
Planetary Motion ◽  
Planetary Theory ◽  
Exponential Series ◽  
Numerical Series ◽  
Satellites Of Jupiter ◽  
General Planetary Theory ◽  
The Right

This paper deals with an iterative version of the general planetary theory. Just as in Airy's Lunar method the series in powers of planetary masses are replaced here by the iterations to achieve improved approximations for the coefficients of planetary inequalities. The right-hand members of the equations of motion are calculated in closed formulas, and no expansion in powers of small corrections to the planetary coordinates is needed. For the N-planet case this method requires the performance of the analytical operations on a computer with power series of 4N polynomial variables, the coefficients being the exponential series of N-1 angular arguments. To obtain numerical series of planetary motion one has to solve the secular system using Birkhoff's normalization or the Taylor series in powers of time. A slight modification of the method in the resonant case makes it valid for the treatment of the main problem of the Galilean satellites of Jupiter.

Application of Hori technique in general planetary theory

1989 ◽  
Vol 44 (3) ◽  
pp. 275-289 ◽  
Author(s):  
Osman M. Kamel
Keyword(s):  
Planetary Theory ◽  
General Planetary Theory

A second order Jupiter-Saturn planetary theory

1982 ◽  
Vol 27 (4) ◽  
pp. 417-430 ◽  
Author(s):  
Osman M. Kamel ◽  
Abdel Aziz Bakry
Keyword(s):  
Second Order ◽  
Planetary Theory

Secular perturbations in general planetary theory

1975 ◽  
Vol 11 (1) ◽  
pp. 131-138 ◽  
Author(s):  
V. A. Brumberg ◽  
L. S. Evdokimova ◽  
V. I. Skripnichenko
Keyword(s):  
Planetary Theory ◽  
Secular Perturbations ◽  
General Planetary Theory

scholarly journals Correspondances Entre Une Theorie Generale Planetaire En Variables Elliptiques Et La Theorie Classique De Le Verrier

1978 ◽  
Vol 41 ◽  
pp. 15-32 ◽  
Author(s):  
L. Duriez
Keyword(s):  
General Theory ◽  
Classical Theory ◽  
Major Axis ◽  
Second Order ◽  
Semi Major Axis ◽  
First Order ◽  
Short Period ◽  
The Masses ◽  
Secular Terms

AbstractIn order to improve the determination of the mixed terms in classical theories, we show how these terms may be derived from a general theory developed with the same variables (of a keplerian nature). We find that the general theory of the first order in the masses already allows us to develop the mixed terms which appear at the second order in the classical theory. We also show that a part of the constant perturbation of the semi-major axis introduced in the classical theory is present in the general theory as very long-period terms; by developing these terms in powers of time, they would be equivalent to the appearance of very small secular terms (in t, t2, …) in the perturbation of the semi-major axes from the second order in the masses. The short period terms of the classical theory are found the same in the general theory, but without the numerical substitution of the values of the variables.

scholarly journals CORRECT REPRODUCTION OF GROUP-INDUCED LONG WAVES

1980 ◽  
Vol 1 (17) ◽  
pp. 47
Author(s):  
N.E. Ottesen Hansen ◽  
Stig E. Sand ◽  
H. Lundgren ◽  
Torben Sorensen ◽  
H. Gravesen
Keyword(s):  
Second Order ◽  
Long Waves ◽  
Wave Problem ◽  
Wave Groups ◽  
Storm Waves ◽  
Slow Drift ◽  
Short Period ◽  
Harbour Resonance ◽  
The Waves ◽  
Wave Phenomena

In nature short period storm waves generate longer waves with periods corresponding to the wave group periods. The long waves are generally referred to as the wave set-down of water level. The set-down term is of second order in the height of the short waves. With first order reproduction of natural storm waves in the laboratory, the setdown bound to the wave groups is not reproduced. As a result, various free waves are generated, propagate towards the model and reflect from the boundaries. These so-called parasitic waves cause an exaggeration of long wave phenomena, such as harbour resonance and slow drift oscillations of moored ships. The parasitic waves can be eliminated by means of compensating free waves imposed on the system by second-order paddle motion reproducing the natural set-down. The control signal for this motion has been calculated and checked by testing. The agreement between calculated and measured results is found to be good. Further, an alternative method for reducing the parasitic wave problem is presented. Utilizing the shoaling properties of the various waves, the influence of parasitic waves can be diminished by generating the waves in somewhat deeper water before they propagate into the shallower model area.

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